Q2 Exercise 2 - Oral Exams 12 Points The oral part of a graduate qualifying exam covers 40 different topics. On the day of the exam, the faculty committee questions each candidate on 3 randomly selected topics. Fortuna Herder, a graduate student pressed for time, prepares for the exam by reviewing 30 topics out of the 40 total. Enter answers to the questions below in the spaces provided. Enter answers to each question part below in the spaces provided. Report any probability as a decimal rounded to 4 places, and report other values rounded to 2 decimal places. Upload a single file with all your work file (pdf, image, code, Markdown) in Blackboard after you submit the exam in Gradescope in order to SHOW YOUR WORK Q2.1 P(Y) 2 Points Let the variable Y represent the number of selected exam topics that Fortuna has reviewed. Find an expression for the probability function of Y, p(y). Enter your answer hereQ1.2 Expected Value 2 Points What is the mean (i.e. expected value) of y? Enter your answer here Q1.3 Standard Deviation 2 Points What is the standard deviation of y? Enter your answer here Q1.4 P(y = 15) 2 Points What is the probability that y = 15? Enter your answer hereQ1 Exercise 1 - Airline Reservations 12 Points A plane has a capacity of 20 passengers. Historical data show that 25% of the people who book a flight do not show up for the flight. Consequently, airline operators often "overbook," allowing more passengers to book a flight than the plane can actually hold. Let the variable Y be the number of passengers who show up for the flight among the 24 who have booked reservations. Enter answers to each question part below in the spaces provided. Report any probability as a decimal rounded to 4 places, and report other values rounded to 2 decimal places. Upload a single file with all your work file (pdf, image, code, Markdown) in Blackboard after you submit the exam in Gradescope in order to SHOW YOUR WORK Q1.1 P(y) 2 Points Find an expression for the probability distribution for Y, p(y). Enter your answer here02.5 Expected Value 2 Points Of the topics selected for Fortune's exam, what is the expected number that she has reviewed? Enter yeur answer here 02.5 Standard Deviation 2 Points Of the topics selected for Fertuna's exam, what Is the standard deviation of the number that she has reviewed? Enter yciur answer here Q1.5 Overbooked! 2 Points What is the probability that more passengers with reservations will show up than the airplane will hold? Enter your answer here Q1.6 Assumptions 2 Points What assumptions have you made in answering the questions in this problem? Be brief - bullet points (or the like) are fine. Enter your answer hereQ2.2 3 for 3 2 Points What is the probability that Fortuna has reviewed all 3 of the randomly selected topics? Enter your answer here Q2.3 2 out of 3 2 Points What is the probability that Fortuna has reviewed exactly 2 of the randomly selected topics? Enter your answer here Q2.4 At least 1 2 Points What is the probability that Fortuna has reviewed at least 1 of the randomly selected topics? Enter your answer here